U.S. Pat. No. 5,994,849 discloses a flat lamp having external electrodes. The discharge vessel comprises a flat baseplate and a trough-shaped front plate with a planar central region, the two plates being sealed to each other in a gas tight manner in the circumferential edge region. Adhesively bonded to the outer side of the baseplate are strip-like aluminum electrodes. This is not practicable in particular in large-area flat lamps having numerous strip-like electrodes, for example typically 42 items in a 17″ flat lamp. One further possibility is to print electrode tracks made of conductive silver paste onto the outer side of the baseplate by means of a screen-printing technique, as is similarly also done in flat lamps having electrodes applied to the inner side of the discharge vessel wall (see, for example, U.S. Pat. No. 6,034,470). As compared with the previous technique, this technique has the advantage that even relatively filigree electrode tracks can be applied easily. However, the relatively high complexity is disadvantageous, particularly since, after the application of the initially pasty electrode tracks, a drying and subsequent baking step are additionally required, the baking generally additionally leading to embrittlement of the discharge vessel consisting of glass. Moreover, in both techniques, an additional measure has to be taken to cover the electrode tracks, in order to ensure the protection against contact and protection against further external influences. Otherwise, in the course of time, undesired changes can occur in the electrode tracks with the result of operational disruption as far as early failures of these lamps.